Yes, technically you can, depending on where in the world you live, and what you do. For example, under Canadian copyright law, you can only read a "reasonable portion" of a book out loud: even though reading out loud doesn't make a copy, and certain tells someone what you know about the book. If you completely re-word each passage, you may or may not be okay. After all, translations into another language usually change almost every word of the original text, but they are still legally considered "derivative works".

In short, copyright law here is nasty, confusing, and horribly nebulous: the courts decide almost everything, like what a "reasonable portion" is, or whether your new version consists of a "significant part" of the original. You'll stay on the right side of the law only if you memorize a lot of case law, have a very good IP lawyer, and/or carefully guess how the judge will rule. Unfortunately, the Copyright Act itself is just a very crude jumping off point; the actual law is inside the minds of the judges who enforce it.

Canadian courts, however, take a very dim view of enforcing non-competes and copyrights of "ideas" in favour of corporations over individuals. I mean, if you actually have a copy of copyrighted code, that's pretty blatant. But merely having learned how a certain framework works, then gaining/maintaining a future employment based on your recollection of that framework (that is, you reimplemented a very similar idea) is not going to be enforced against that individual.

Corporations that cherry-pick competitors' best talents solely to learn copyrights will have their hands slapped, but the individual is rarely going to be punished for anything. There is a certain "right to work" (which is separate from the union-busting laws of the same name) which Canadian courts feel are superior to any contract to the contrary, thus any contract stating you cannot use knowledge gained in a position in future positions are generally found to be null and void (or at least that part is found that way).

Disclaimer: IANAL. This is just what my current employer has told me (on my first day at work, I might add).

You've phrased this as a declaratory statement, but then you fall back on the fact that the entire thing is heresay from your employer.
The whole notion that "Candian courts value X over Y" falls into the "carefully guess the will of the judge" category; remember that any precedent can be overturned whenever a judge feels it's appropriate. Judges just aren't predictable: they can rule how they feel is appropriate, outside of external influences. That's good in some cases, bad in others. One of the ways that it's bad is lack of predictablilty: the notion of precedent mitigates, but does not solve, this problem.

Moreover, it's quite possible your employer's opinions of the Canadian courts are wrong. He does, after all, have a vested interest in getting you to divulge information about past workplaces: and little to lose until you leave. See if he changes his tune during the exit interview.